Update cookies preferences

Mathematics & Climate [Paperback / softback]

4.22/5 (18 ratings by Goodreads)
,
  • Format: Paperback / softback, 315 pages, height x width x depth: 229x152x15 mm, weight: 582 g
  • Pub. Date: 30-Oct-2013
  • Publisher: Society for Industrial & Applied Mathematics,U.S.
  • ISBN-10: 1611972604
  • ISBN-13: 9781611972603
Other books in subject:
  • Paperback / softback
  • Price: 81,10 €
  • This book is not in stock. Book will arrive in about 2-4 weeks. Please allow another 2 weeks for shipping outside Estonia.
  • Quantity:
  • Add to basket
  • Delivery time 4-6 weeks
  • Add to Wishlist
Mathematics & ClimateLarger Image
  • Format: Paperback / softback, 315 pages, height x width x depth: 229x152x15 mm, weight: 582 g
  • Pub. Date: 30-Oct-2013
  • Publisher: Society for Industrial & Applied Mathematics,U.S.
  • ISBN-10: 1611972604
  • ISBN-13: 9781611972603
Other books in subject:
Permanent link: https://www.kriso.lv/db/9781611972603.html
Keywords:
Mathematics and Climate is a timely textbook aimed at students and researchers in mathematics and statistics who are interested in current issues of climate science, as well as at climate scientists who wish to become familiar with qualitative and quantitative methods of mathematics and statistics. The authors emphasize conceptual models that capture important aspects of Earth's climate system and present the mathematical and statistical techniques that can be applied to their analysis.

Topics from climate science include the Earth's energy balance, temperature distribution, ocean circulation patterns such as El NiñoâSouthern Oscillation, ice caps and glaciation periods, the carbon cycle, and the biological pump. Among the mathematical and statistical techniques presented in the text are dynamical systems and bifurcation theory, Fourier analysis, conservation laws, regression analysis, and extreme value theory.

The following features make Mathematics and Climate a valuable teaching resource:

Issues of current interest in climate science and sustainability are used to introduce the student to the methods of mathematics and statistics. The mathematical sophistication increases as the book progresses; topics can thus be selected according to interest and level of knowledge. Each chapter ends with a set of exercises that reinforce or enhance the material presented in the chapter and stimulate critical thinking and communication skills. The book contains an extensive list of references to the literature, a glossary of terms for the nontechnical reader, and a detailed index.
List of Figures xi
Preface xvii
1 Climate and Mathematics 1(12)
1.1 Earth's Climate System
1(1)
1.2 Modeling Earth's Climate
2(1)
1.3 Conceptual Models
3(2)
1.4 Climate and Statistics
5(1)
1.5 Climate Variability and Climate Change
6(2)
1.6 Models from Data
8(2)
1.7 Exercises
10(3)
2 Earth's Energy Budget 13(16)
2.1 Solar Radiation
13(1)
2.2 Energy Balance Models
14(2)
2.3 Basic Model
16(1)
2.4 Greenhouse Effect
17(1)
2.5 Multiple Equilibria
18(1)
2.6 Budyko's Model
19(1)
2.7 Snowball Earth
20(1)
2.8 Bifurcation
21(2)
2.9 Exercises
23(6)
3 Oceans and Climate 29(12)
3.1 Ocean Circulation
29(2)
3.2 Temperature
31(1)
3.3 Salinity
32(1)
3.4 Box Models
33(3)
3.5 One-Dimensional Model
36(3)
3.6 Exercises
39(2)
4 Dynamical Systems 41(22)
4.1 Autonomous Differential Equations
41(3)
4.2 Geometrical Objects
44(4)
4.3 Critical Points
48(1)
4.4 Periodic Orbits
49(2)
4.5 Dynamics near Critical Points
51(1)
4.6 Planar Case
52(4)
4.7 Nonlinear Systems
56(2)
4.8 Exercises
58(5)
5 Bifurcation Theory 63(14)
5.1 Bifurcation
63(1)
5.2 Examples
64(9)
5.3 From Examples to the General Case
73(1)
5.4 Bifurcation Points
74(1)
5.5 Hopf Bifurcation Theorem
74(1)
5.6 Exercises
75(2)
6 Stommel's Box Model 77(10)
6.1 Stommel's Two-Box Model
77(1)
6.2 Dynamical System
78(4)
6.3 Bifurcation
82(1)
6.4 Comments
82(1)
6.5 Exercises
83(4)
7 Lorenz Equations 87(8)
7.1 Lorenz Model
87(1)
7.2 Preliminary Observations
88(1)
7.3 Equilibrium Solutions
89(2)
7.4 Numerical Experiments
91(1)
7.5 Exercises
92(3)
8 Climate and Statistics 95(10)
8.1 Challenges for Statistics
95(3)
8.2 Proxy Data
98(3)
8.3 Reanalysis
101(1)
8.4 Model Skill
102(1)
8.5 Exercises
103(2)
9 Regression Analysis 105(12)
9.1 Statistical Modeling
105(3)
9.2 Linear Regression
108(2)
9.3 Simple Linear Regression
110(1)
9.4 Regression Diagnostics
111(2)
9.5 Exercises
113(4)
10 Mauna Loa CO2 Data 117(6)
10.1 Keeling's Observational Study
117(1)
10.2 Assembling the Data
118(1)
10.3 Analyzing the Data
118(4)
10.4 Exercises
122(1)
11 Fourier Transforms 123(18)
11.1 Fourier Analysis
123(1)
11.2 Trigonometric Interpolation
124(1)
11.3 Discrete Fourier Transform
125(1)
11.4 Fast Fourier Transform
126(1)
11.5 Power Spectrum
127(1)
11.6 Correlation and Autocorrelation
128(2)
11.7 Fourier Series and Fourier Integrals
130(1)
11.8 Milankovitch's Theory of Glacial Cycles
131(6)
11.9 Exercises
137(4)
12 Zonal Energy Budget 141(18)
12.1 Zonal Energy Balance Model
141(5)
12.2 Legendre Polynomials
146(2)
12.3 Spectral Method
148(2)
12.4 Equilibrium Solutions
150(1)
12.5 Temperature Profile
151(1)
12.6 Assessment
152(2)
12.7 Exercises
154(5)
13 Atmosphere and Climate 159(6)
13.1 Earth's Atmosphere
159(1)
13.2 Pressure
160(1)
13.3 Temperature
160(2)
13.4 Atmospheric Circulation
162(2)
13.5 Exercises
164(1)
14 Hydrodynamics 165(18)
14.1 Coriolis Effect
165(4)
14.2 State Variables
169(1)
14.3 Continuity Equation
170(1)
14.4 Equation of Motion
171(2)
14.5 Other Prognostic Variables
173(1)
14.6 Equation of State
173(1)
14.7 Coupling Ocean and Atmosphere
174(1)
14.8 Need for Approximations
174(1)
14.9 Shallow Water Equations
174(3)
14.10 Further Approximations
177(1)
14.11 Boussinesq Equations
178(1)
14.12 Exercises
179(4)
15 Climate Models 183(10)
15.1 Climate Models as Dynamical Systems
183(2)
15.2 Dimension Reduction: Lorenz Model
185(4)
15.3 Abstract Climate Models
189(2)
15.4 Exercises
191(2)
16 El Nino-Southern Oscillation 193(20)
16.1 El Nino
193(2)
16.2 Recharge-Oscillator Model
195(3)
16.3 Delayed-Oscillator Model
198(6)
16.4 Delay Differential Equations
204(2)
16.5 Numerical Investigations
206(2)
16.6 Exercises
208(5)
17 Cryosphere and Climate 213(10)
17.1 Cryosphere
213(1)
17.2 Glaciers, Ice Sheets, and Ice Shelves
214(1)
17.3 Sea Ice
215(5)
17.4 Exercises
220(3)
18 Biogeochemistry 223(14)
18.1 Biosphere and Climate
223(1)
18.2 Carbon Cycle
224(3)
18.3 Carbon Transport into the Deep Ocean
227(1)
18.4 Ocean Plankton
228(2)
18.5 Algal Blooms
230(5)
18.6 Exercises
235(2)
19 Extreme Events 237(14)
19.1 Climate and Weather Extremes
237(3)
19.2 Exceedance
240(2)
19.3 Tail Probabilities and Return Periods
242(2)
19.4 Order Statistics, Extreme Value Distribution
244(4)
19.5 Exercises
248(3)
20 Data Assimilation 251(18)
20.1 Data Assimilation and Climate
251(1)
20.2 Example
252(2)
20.3 Bayesian Approach
254(1)
20.4 Sequential Data Assimilation
255(2)
20.5 Kalman Filtering
257(2)
20.6 Numerical Example
259(2)
20.7 Extensions
261(2)
20.8 Data Assimilation for the Lorenz System
263(2)
20.9 Concluding Remarks
265(1)
20.10 Exercises
265(4)
A Units and Symbols 269(4)
B Glossary 273(6)
C MATLAB Codes 279(4)
C.1 MATLAB Code for Lorenz Equations
279(1)
C.2 MATLAB Code for Regression Analysis
280(1)
C.3 MATLAB Code for Delay Differential Equations
280(3)
Bibliography 283(8)
Index 291
Maurizio Falcone is Professor of Numerical Analysis in the Mathematics Department of Sapienza University of Rome. He is an associate editor for the journal Dynamic Games and Applications and was a member of the scientific board of the CASPUR Consortium for Scientific Computing (2002-2012) and on the steering committee of the ESF Network ""Optimization with PDE Constraints""; (2008-2012). He has been an invited professor at ENSTA (Paris), the IMA (Minneapolis), Paris 6 and 7, PIMS (Vancouver and Banff), the Russian Academy of Sciences (Moscow), and UCLA and has coordinated international research projects with France, Russia, and the European Community (Marie Curie). He is the author of about 60 papers in international journals. His main research areas are numerical analysis, PDEs, control theory and differential games, and image processing.

Roberto Ferretti is Associate Professor in Numerical Analysis at Roma Tre University. He has spent invited research periods at UCLA, IHP Paris, Goroda Pereslavlya University (Pereslavl-Zalessky, Russia),Technical University of Madrid, ENPC Paris, and ENSTA Paris. He is the author of about 35 research papers in international journals and in proceedings, most of which are on semi-Lagrangian schemes. His main research areas are numerical analysis, PDEs, control theory, image processing, and environmental fluid dynamics.